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The Effect of The Learning Cell Model
on Students’ Mathematical Communication Skills
Gusni Satriawati, Adelina Fitriyani, Kadir
Syarif Hidayatullah State Islamic University Jakarta, Jl. Ir. H. Djuanda 95, Ciputat, Indonesia
E-mail: [email protected]
Abstract
The competence of mathematical communication skill is one of the main factors in learning Mathematics; however,
the reality in learning mathematics shows that the students’ ability of mathematical communication is still low. The
main issues of this study is to analyse the students 'mathematical communication skills using The Learning Cell
model and expository learning and to analyze the effect of the application of The Learning Cell model on students'
mathematical communication skills. The research method used was a quasi-experimental method with research
design of Two Group Randomized Subject Post-Test Only. To know the effect of The Learning Cell model's
treatment of mathematical communication skills used Effect Size formula. The total sample was 87 students
consisted of 44 students of experimental group and 43 students of control group. The technique of data collection
for students' mathematical communication skills used the test instrument on the sub-subject of building a flat side
space. The results show that the students’ mathematical communication skills are taught with The Learning Cell
model is higher than the students' mathematical communication skills with those who taught with expository
learning and the Effect Size is in the medium category. The indicators of mathematical communication skills in this
research are: (1) representing real objects, drawing diagrams or tables in the form of ideas and mathematical
symbols, (2) explaining ideas, situations and mathematical relations in writing using real objects, images, and
algebraic expressions, (3) declare everyday events in language or mathematical symbols or arrange mathematical
models of events. So, The Learning Cell model is one of mathematics learning that can be used to improve the
students' mathematical communication skills.
Keywords: The learning cell model, mathematical communication skills, build a flat side space, effect size
1 INTRODUCTION
Communication skill is one of the aims of
mathematics learning, so needed a good ability to
communicate for achieving the purpose of
mathematics learning. The importance to have the
communication skills, especially in Math lessons
which are reinforced by the experts’ opinion. Prayitno
(2013: 566) states that mathematical communication
is needed by the people to communicate ideas or to
solve mathematical problems, either in spoken,
written, or in visual, such as in mathematical learning
or outside of it. According to Polla (Isrok'atun, 2009:
8) mathematical communication is one of the
important factors in the learning process of
mathematics both inside and outside the classroom.
Communication handles an important action in
mathematics. Anyone who has a special interest in
mathematics will need communication should always
add his/her information as much as possible.
However, the reality in learning mathematics,
the students’ communication skills are still in low
level. Based on the interview results with Math
teachers at SMPN 3 Tangerang Selatan, students are
rarely use mathematical communication skills, so
they are difficult to communicate in mathematics,
using symbols and translating and developing them in
ordinary language or others. This case as result of the
teaching applied in the school is the expository or
teacher centered learning, where the teacher is still
dominant in explaining the subject matter in the class
and the students get less opportunity to explore their
skills to communicate their ideas in mathematic.
Awa's research result (2013) suggests that the highest
indicators of students’ mathematical communication
3rd International Conferences on Education in Muslim Society (ICEMS 2017)
Copyright © 2018, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Advances in Social Science, Education and Humanities Research, volume 115
77
skills are the abilities to declare or illustrate
mathematical models into the form of mathematical
ideas. According to LACOE, the appropriate way to
develop students' mathematical communication skills
is in group discussion. In the process of discussion
will exchange of ideas and opinion between students.
This will provide an opportunity for students to build
up their understanding and communication skills of
mathematic.
Indicators of mathematical communication
skills used in this research are:
1) Represents real objects, images, diagrams or
tables in the form of ideas and mathematical
symbols
2) Describe ideas, situations and mathematical
relationships in writing using real objects, images,
and algebraic expressions
3) Stating daily occurrence in a language or
mathematical symbol or composing mathematical
model of an occurrence
An alternative model of learning that can
improve students' communication skills is The
Learning Cell model created by Goldschmid in 1976
from Switzerland and then developed again in China
by Yu, Yang, and Cheng in 2015. The Learning Cell
model is a series of learning activities where at each
stage of learning requires students communicate their
own ideas and opinions to other students actively
(Goldschmid, 1976: 20).
The Steps of The Learning Cell in this study are
as follows:
1) Openness
Teachers provide problems those produce variety
responses from students about the issues or topics
given at the beginning of the lesson. From their
answers, then the teachers give tentative or
temporary conclusion. Students list the questions
after looking at the problems which the teachers
revealed, and the question can be asked to other
groups to get the answers.
Figure 1. The Openness of the Learning Cell Principles
The open source of learning according to the
picture above comes from generative information,
learning tools that can openly access learning
content, an ontology environment and classroom
learning activities. Educators present an open
source of learning so that it can trigger various
responses from learners who can develop an
existing learning resource.
2) Social
Then the teacher divides some groups are even
numbered and odd group. The odd group discuss
about the content of lesson A, while the even
group learn lesson content B. Then each student
in the group exchanges information about the
content of the lesson discussed. In other hands,
each group has to make 2 questions; the odd group
makes the question for material B which the even
group discussed, and also even group ask for the
odd group material.
3) Evolvable & Context-Aware
After learning the lesson content and preparing 2
questions, every student in group pairs to the other
group. One of odd group paired with who in even
group (small groups). Activities include asking
and answering questions those prepared each
other between the groups based on their own topic
or material. During this process, the teacher
supervises from one couple to another; provides
confirmation or feedbacks to the students.
Context-Aware is a contextual awareness when
students realize what learning or learned at the
meeting. Contextual awareness showed from the
student's question whether they really investigate
for the material discussed or from their reply.
4) Cohesive
All students summarize the materials in
accordance with the results of questions and
answers with friends. The results of these
conclusions are summarized, which is used as the
learning resources expand in accordance with the
learners’ understanding. The conclusions are
presented by one member of the group in front of
the class.
The application of The Learning Cell model is
expected to get the widest opportunity for students to
express their mathematical ideas, expresses or clarify
their ideas both orally and in written one. Marta
Cahyaningrum, et al. (2012) in her research explained
that the average learning outcomes of students whose
learning using The Learning Cell learning is higher
than the average of student learning outcomes that get
conventional learning. Rita Khotimah & Mukhafifah
(2011) in their research reveal that there is the effect
Advances in Social Science, Education and Humanities Research, volume 115
78
of student learning activity on student's mathematics
learning achievement.
Based on the above description, the researcher
feels the need to do research with the title “The Effect
of The Learning Cell Model to Students’
Mathematical Communication Skills”.
The problems that will be discussed in this
research are (1) how is the students’ mathematical
communication skill those using The Learning Cell as
learning model and those using conventional
learning? (2) Are the students’ mathematical
communication skills those use The Learning Cell as
learning model higher than those use conventional
learning model?
The purposes of this research are: (1) to analyze
the students’ mathematical communication skills of
the students whose use The Learning Cell and
conventional learning model, (2) to analyze the effect
of the Learning Cell Model for students'
mathematical communication skills.
While the hypothesis in this study, namely "The
students' mathematical communication skills those
using The Learning Cell are higher than those using
conventional learning model".
2 METHODS
The method used in this study is the quasi-
experimental method, which the researchers
unavailable to fully control to the other factors that
influence the variables and experimental conditions.
Selection method based on considering the research
characteristic which intended to analyze the effect of
application of The Learning Cell to students'
mathematical communication skills. The research
design used was posttest-only control group design by
taking two randomly selected classes/groups to be
used as control group and experimental group. In the
experimental group was given special treatment in the
form of learning by using The Learning Cell.
Meanwhile in the control group, researchers
conducted a learning process used expository
strategy. Then, both groups were given a post-test to
obtain the empirical evidence as seen in the final
result, to know whether there is a difference between
the experimental group and the control group.
The affordable population in this study were all
students in SMP Negeri 3 Tangerang Selatan class
VIII registered in the even semester of academic year
2016/2017 consisting of 9 classes. The sample of this
study was chosen by using simple random sampling
technique from an affordable population.
The instrument used in this study is a test
instrument in the form of an essay test to measure the
mathematical communication skills of junior high
school students. The instrument consisted of 6 point-
shaped questions to be given to the experimental
group and the control group after both of them had
completed the overall learning with the subject of
building a flat side room. Instruments tested to both
groups have previously been designed by the
researcher by making a grid on the subject of building
a flat side room adapted to the indicator of the
mathematical communication ability to be measured.
After that, the researchers made scoring guidelines
for assessing student answers. Scoring guidelines
required to measure students' mathematical
communication skills on each item.
Before the instrument used, firstly the
instrument is piloted. This trial is intended to obtain
validity, distinguishing power, difficulty, and
reliability of the instrument. The data obtained were
analyzed using the test of difference of two averages.
The test formula used was t-test. To know the effect
of The Learning Cell model was used effect Size
formula (r2) (Kadir, 2015).
3 RESULTS AND DISCUSSION
Based on the data processing on the post-test
score on the aspect to be measured, those aspects of
the students' mathematical communication skills,
obtained post-test score for experimental group and
control group in Table 1 below.
Advances in Social Science, Education and Humanities Research, volume 115
79
Table 1. Comparison of Mathematical Communication Skills of Students of Experiment Class and Control Class
No. Indicators
Experiment Class Control
Class
�̅� % �̅� %
1.
2.
3.
Represents real objects, drawings,
and diagrams in the form of ideas and
mathematical symbols
Explain ideas, situations and
mathematical relationships in
writing using real objects, images,
and algebraic expressions
Stating the daily occurrence in a
language or mathematical symbol or
composing mathematical model of
occurrence
2,24
2,50
3,29
56,10
62,50
82,27
1,74
2,06
2,69
43,47
51,42
67,33
Avarage 2,68 66,96 2,16 54,07
Table 1 shows the acquisition of percentage of
first indicator of mathematical communication skills
that represent real object, drawing, and diagram in the
form of idea and or mathematical symbol in
experiment class is higher than control class, the
percentage equal to 56,10%. It is caused the students
in the experimental class who use The Learning Cell
especially at the stage of Openness, Social, Evolvable
& Context-Aware and Cohesive make students
command in representing images into ideas or
mathematical symbols. In addition, they command to
work out the problem systematically during the
learning activities and always concluding what has
been completed so that they can communicate
mathematical ideas well. But in the control class,
these activities are rarely performed. In indicator 2 it
explains ideas, situations, and mathematical relations
in writing using real objects, images, and algebraic
expressions, the percentage of experimental class is
62,50% better than control class that is 51,42%.It is
caused by the learning process in the experimental
class that apply Learning Cell model especially in
Social, Evolvable & Context-Aware and Cohesive
there are activities where students are given various
information related to the building of flat side space
either in the form of statement relating to the daily
occurrence and image description, then students are
trained to do it by writing in advance what
information is contained in the matter so they can use
the information available to answer the problem.
They command to solve the problems using their own
language and explain their answers with drawings or
diagrams if necessary to communicate their
understanding and mathematical ideas to their
classmates. It contrast to the control class in the
learning who does not involve the way to
communicate mathematical ideas with images,
diagrams or tables, the students feel little difficult
when finding the problem assigned to illustrate in the
form of drawings, diagrams, tables, or algebraic
expression resulting in a picture that has not made
perfect. In indicator 3 it states daily occurrence in
language or mathematical symbol or arrange
mathematical model of an occurrence, the percentage
of students' mathematical communication skills in
experiment class is better than control class, that is
82,27%. Because the experimental class students,
especially at the level of Openness, Social, Evolvable
& Context-Aware and Cohesive are familiar with
issues related to daily life, so they can solve problems
related to daily problems or mathematical situations
and then solve them with the language of
Advances in Social Science, Education and Humanities Research, volume 115
80
mathematics or compile a mathematical model to
solve a problem. While the control class students in
the learning process only emphasizes the formulas
that must be known to solve the problem it caused the
control class students have not been able to declare a
mathematical situation, especially in daily life and
they completed according to their own answers. Table 1 presents the comparison of students'
mathematical communication skills of the experimental class and control classes based on the three indicators. The percentage of achievement of the students' mathematical communication skills test in the experimental class is 66,96% while the percentage of students' mathematical communication skills in the control class is 54,07% or in other words the percentage of mathematical communication skills of the experimental class is higher than the students' mathematical communication in control class.
After hypothetical test of overall mathematical communication skills, tcount = 3,138 is greater than ttable = 1.663 so it can be concluded that H0 is rejected, while H1 is accepted. H1 states that with 5% error degree, the average value of the mathematical communication skills of the students whose learning using The Learning Cell as learning model is higher than using expository. In general, after analysing the results of research, there are several things that cause differences in the average value of the experimental class and control class, one of the reasons is the learning process conducted on the experimental class and control class. This finding means that the learning process with The Learning Cell that contains the Social, Evolvable, and Context-Aware stages is more useful to the students to improve their mathematical communication skills than expository learning. These findings are also in line with the opinion of LACOE (Mahmudi, 2009) which suggests that the appropriate way to increase the mathematical communication skills is in group discussions. This is also in line with Goldschmid's (1972) states that The Learning Cell can improve students’ learning achievement more significant when given "unannounced examination" than the students who use conventional learning. In addition to this opinion, the findings of this study also correspond to research conducted by Marta Cahyaningrum, et al. (2012) who found that the average learning outcomes of students whose learning using The Learning Cell were higher than the average learning outcomes of students who get conventional learning. During the learning process, students who use The Learning Cell model tend to be more active in exploring information and knowledge that has not been owned. These findings are in line with research conducted by Rita Khotimah & Mukhafifah (2011) founded that the influence of student learning activities on student learning
achievement mathematics. However, the findings of this study are not in line with the research conducted by Awa (2013) founded that the highest indicator of the students’ mathematical communication skills is to express or illustrate mathematical models into the form of mathematical ideas.
4 CONCLUSION
Based on the results of the study on the
mathematical communication skills of students in
SMP Negeri 3 Tangerang Selatan, it can be drawn
conclusions as follow:
1. The students' mathematical communication skills
who are taught with The Learning Cell model
classified as good compared to conventional
learning strategies. The highest to the lowest
achievement of the indicators of mathematical
communication skills of the two learning are
similar. The highest achievement obtained on the
indicator of the event's mathematical and the
contents of the event's mathematical relationships.
Or tables in the form of ideas and mathematical
symbols.
2. Learning uses The Learning Cell model
influences students' mathematical communication
skills. The students' mathematical communication
skills are taught with learning techniques of The
Learning Cell model is more effective in
improving students' mathematical communication
skills than those are taught with conventional
learning models.
5 ACKNOWLEDGEMENTS
Firstly, we would like to thank the teachers and
students at SMP 3 Tangerang Selatan who have given
their support during the research. Secondly, a great
thank delivers to colleagues in the department of
mathematics education who have sharing their ideas.
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